Advanced Differentiation: AP Calculus AB: Free Course

About this course

Differentiating a complicated expression starts with recognizing its structure. This course develops the chain rule, implicit and inverse differentiation, combined rules and higher derivatives. Study the complete public source playlist from Khan Academy in English, with all 38 recordings available in the on-site classroom. Lessons retain their original titles and source order, including worked examples, introductions and repeated entries.

Course at a glance

What you’ll learn

• Identify composite functions and apply the chain rule.
• Differentiate implicit relationships and inverse functions.
• Combine product, quotient and chain rules strategically.
• Calculate higher derivatives and explain rule-based errors.

Skills you’ll gain

• Chain rule
• Implicit differentiation
• Inverse derivatives
• Higher derivatives

Course Overview

Composite functions provide the central thread. The early examples identify inner and outer functions and address common chain-rule errors before applying the rule to trigonometric, exponential, logarithmic and radical expressions. Implicit differentiation extends the method to relationships that have not been solved explicitly for one variable. Inverse-function lessons use equations and tables as well as inverse trigonometric functions. Later examples combine several rules, sometimes after algebraic rewriting, and include second derivatives of implicit equations. The closing proof-oriented material connects differentiability with continuity and revisits the reasoning behind differentiation rules. This is a focused advanced-differentiation sequence within the AP Calculus AB context, not the entire AP curriculum. Keep the variable of differentiation and each dependency visible, especially when a product, composition and implicit relationship occur together.

How to study the course

• Videos 1–9: this part of the source list includes “Chain rule” through “Derivative of log_x (for any positive base a­1)”. Identify the function, variable and conditions. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 10–19: this part of the source list includes “Exponential functions differentiation” through “Derivatives of inverse functions: from equation”. Connect the method to the meaning of the problem. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 20–28: this part of the source list includes “Derivatives of inverse functions: from table” through “Applying the chain rule twice”. Rework a demonstration with a changed parameter. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 29–38: this part of the source list includes “Derivative of e_____cos(e_)” through “Quotient rule from product & chain rules”. Check the result and explain its interpretation. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.

Who is this for?

This course suits learners with algebra and trigonometry preparation who want the specific calculus topic in the title. It also provides a recorded reference for revisiting a topic after an earlier lesson or study attempt. Choose examples appropriate to your background and allow time to work through the method instead of judging understanding only by how familiar the terminology sounds.

Before you start

Comfort manipulating algebraic expressions and interpreting functions is important. Review the prerequisite calculus stated by a lesson before using an advanced technique.

Put the lessons into practice

Choose one composite expression, one implicit equation and one example requiring two differentiation rules. Annotate the dependency structure before calculating. Check an answer by comparing with an explicitly solved form where that is feasible. Finish by writing a deliberately incorrect derivative, locating the missing factor or mistaken dependency and explaining the correction.

This optional study activity is provided by WikiFree for independent practice. Keep your working notes and use the relevant classroom recording to check a step, definition or interpretation. It is not an instructor-marked assignment.

Certificate / Assessment

Watching the public videos and using WikiFree completion tracking does not award a certificate, academic credit, an examination voucher or instructor assessment. Use your practice output to review what you can explain and repeat independently. The recorded lessons provide study material; completion tracking records your progress through that material.

Frequently asked questions

Provider: Khan Academy. Videos play from the Khan Academy channel on YouTube.